A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented by generators and relations.

We show that proofs in the intuitionistic propositional logic factor through interpolants-in this way we prove a stronger interpolation property than the usual one which gives only the existence of interpolants.Translating that to categorical terms, we show that Pushouts (bipushouts) of bicartesian closed categories have the interpolation property (Theorem 3.2).

Tekst je prosireno obrazlozenje predlozene teme projekta koja se bavi mogucnoscu prihvatanja i stabilizacije liberalnih obrazaca distribucije u drustvima u tranziciji. Srbija je u ovom pogledu iz niza razloga poseban slucaj. Liberalizacija ovih drustava je uvek neizvestan proces jer zavisi od dve vazne pretpostavke. Prva je olicena u paradoksu ovakvog vida tranzicije koji se sastoji u postojanju ili nepostojanju politickih poticaja da se neke sfere zivota osamostale od procesa politickog odlucivanja. Druga je da liberalizacija moze biti samo destruktivna. Naime, minimalni (...) ucinci liberalizacije, uspostavljanje obrazaca odgovornosti i javne sfere, mogu u svom krajnjem ishodu imati neliberalne ucinke. No, pored svega, stabilnost liberalnih poredaka pociva upravo na otvorenoj mogucnosti stalnog preispitivanja i korigovanja obrazaca raspodele koji su ugradjeni u institucionalne mehanizme ovih drustava. (shrink)

Tekst razmatra Rolsovu ideju javnog uma kao sredisnji deo njegove koncepcije politickog liberalizma. Ideja javnog uma je shvacena dvostruko, kao norma opravdanja i kao politicki ideal. U tekstu su takodje razmotrene neke kritike Rolsove koncepcije i naznaceni moguci nacini na koji se Rols moze odbraniti od njih. Osnovne teze u tekstu su da se Rolsova koncepcija javnog uma moze odbraniti od standardnih kritika, ali i da sama razotkriva ogranicenja politickog ideala liberalne demokratije. Dosledno shvacen, politicki ideal liberalne demokratije mora se (...) odreci pretenzija na moralnu superiornost i oslanjati se na moralni konsenzus koji moze biti potvrdjen javnim umom politickog drustva.. (shrink)

We investigate the universal fragment of intuitionistic logic focussing on equality of proofs. We give categorical models for that and prove several completeness results. One of them is a generalization of the well known Yoneda lemma and the other is an extension of Harvey Friedman's completeness result for typed lambda calculus.

The existence of a topological double-covering for the GL(n, R) and diffeomorphism groups is reviewed. These groups do not have finite-dimensional faithful representations. An explicit construction and the classification of all\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overline {SL} $$ \end{document}(n, R), n=3,4 unitary irreducible representations is presented. Infinite-component spinorial and tensorial\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overline {SL} $$ \end{document} fields, “manifields”, are introduced. Particle content of the ladder manifields, as given by (...) the\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overline {SL} $$ \end{document}(3, R) “little” group, is determined. The manifields are lifted to the corresponding world spinorial and tensorial manifields by making use of generalized infinite-component frame fields. World manifields transform w.r.t. corresponding\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overline {Diff} $$ \end{document} representations, which are constructed explicitly. (shrink)